Turbulent flow in circular tubes

An exclusively analytical treatment of heat and mass transfer in turbulent flow in pipes fails because to date the turbulent shear stress Tl j = —Qw w p heat flux q = —Qcpw, T and also the turbulent diffusional flux j Ai = —gwcannot be investigated in a purely theoretical manner. Rather, we have to rely on experiments. In contrast to laminar flow, turbulent flow in pipes is both hydrodynamically and thermally fully developed after only a short distance x/d 10 to 60, due to the intensive momentum exchange. This simplifies the representation of the heat and mass transfer coefficients by equations. Simple correlations, which are sufficiently accurate for the description of fully developed turbulent flow, can be found by 

3 Convective heat and mass transfer. Single phase flow 

The friction factor cf is linked to the resistance factor C t0 dnL = Ap (d27r/4),  

184 Re 1/5 valid for Re 104 for turbulent tubular flow, we obtain the following for the Nusselt number 

A relationship that approximately agrees with equation (3.262) was recommended by Kraussold [3.33] in 1933, based upon his own experiments and those of others. The equation was first communicated in the form presented here by McAdams [3.34] in 1942. ft presumes small temperature differences between the wall and the fluid, and is valid in the region 

---

Expressions for turbulent flow in circular tubes were determined from experimental data. One such equation (using Nu as a function only of Re and Pr) is... 

---